Question

What is the value of the x variable in the solution to the following system of equations?

4x + 8y = 8
x + 2y = 2

Answer 1

well what method do you want to use in order to find out what x is?

Answer 2

substitution

Answer 3

OK so we must isolate y in either the first or second equation and then substitute it to the other one. Which equation do you want to isolate y ?

Answer 4

8

Answer 5

the first one

Answer 6

4x + 8y = 8


Ok so we want y bu itself right either on the left side or the right side. Since y is in the left side lets keep it there...

First subtract 4x to both sides.

4x + 8y = 8
4x-4x + 8y = 8-4x
8y = 8-4x

Ok here is a trick since we have 2y on the second one we can then divide a number on this equation to get 2y right? that number is 4 . Lets divide both sides by 4

8y/4 = (8-4x )/4

2y=2-x

Answer 7

Do you follow along?

Answer 8

Yes i think

Answer 9

ok so the first equation is now
2y=2-x
and the second one is
x + 2y = 2

The first equation is telling us that when we have 2y anywhere
we can replace that 2y with 2-x

Looks like we have a 2y in the second equation right?

x + 2y = 2

Let's replace that 2y with 2-x

x + 2- x = 2

Answer 10

look at that we have a positive x and a negative x that cancel each other out.

and we have 2=2

Answer 11

seems to me that both equations are the same.

because when does 2=2 ? always right 2 will always equal 2

Answer 12

So by switching the same signs to different sides and then dividing we get 2 ?

Answer 13

Thank you RyanL

Answer 14

well no it means that we have an infinite number of solutions and by solution we mean where both equation cross.

since both equations are the same they cross over each other in every single point
so essentially we have
\[x=\infty \]

Answer 15

4x + 8y = 8
x + 2y = 2

if we multiply the second equation by 4 we get

4x + 8y = 8
4x + 8y = 8

Answer 16

Good job @RyanL.
There is an infinite number of solutions since you really only have one equation with two variables.
\(x = \infty\) is not a correct statement. What you were trying to state is that there is an infinite number of solutions.

Answer 17

how would you write that with terms?

Answer 18

that a there are infinite number of solutions.

Answer 19

If you had an equation in just x, and the solution is an infinite number of answers, usually that means all real numbers.
Here, x can be any real number, but each y has to be the correct y for each ordered pair.
I just state "infinite number of solutions."
You can say every point on the line x + 2y = 8 is a solution.

Answer 20

Thanks....looking back writing x=infinity makes it sound like if there is an Asymptote. Thanks for the help.